Properties

Label 429.2.t.a.296.20
Level $429$
Weight $2$
Character 429.296
Analytic conductor $3.426$
Analytic rank $0$
Dimension $104$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(296,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.296");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(104\)
Relative dimension: \(52\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 296.20
Character \(\chi\) \(=\) 429.296
Dual form 429.2.t.a.329.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.716153 + 0.413471i) q^{2} +(1.20308 - 1.24603i) q^{3} +(-0.658083 + 1.13983i) q^{4} +3.60945 q^{5} +(-0.346391 + 1.38979i) q^{6} +(1.45351 - 2.51755i) q^{7} -2.74228i q^{8} +(-0.105197 - 2.99816i) q^{9} +O(q^{10})\) \(q+(-0.716153 + 0.413471i) q^{2} +(1.20308 - 1.24603i) q^{3} +(-0.658083 + 1.13983i) q^{4} +3.60945 q^{5} +(-0.346391 + 1.38979i) q^{6} +(1.45351 - 2.51755i) q^{7} -2.74228i q^{8} +(-0.105197 - 2.99816i) q^{9} +(-2.58492 + 1.49241i) q^{10} +(-3.01848 + 1.37434i) q^{11} +(0.628544 + 2.19131i) q^{12} +(2.11573 - 2.91953i) q^{13} +2.40394i q^{14} +(4.34246 - 4.49750i) q^{15} +(-0.182314 - 0.315778i) q^{16} +(-0.309839 + 0.536657i) q^{17} +(1.31499 + 2.10364i) q^{18} +(-1.18049 + 2.04467i) q^{19} +(-2.37532 + 4.11418i) q^{20} +(-1.38826 - 4.83994i) q^{21} +(1.59344 - 2.23229i) q^{22} +(-5.10705 + 2.94856i) q^{23} +(-3.41697 - 3.29918i) q^{24} +8.02816 q^{25} +(-0.308046 + 2.96563i) q^{26} +(-3.86236 - 3.47594i) q^{27} +(1.91306 + 3.31352i) q^{28} +(3.36278 + 5.82450i) q^{29} +(-1.25028 + 5.01638i) q^{30} -5.67006i q^{31} +(5.01089 + 2.89304i) q^{32} +(-1.91900 + 5.41456i) q^{33} -0.512438i q^{34} +(5.24637 - 9.08699i) q^{35} +(3.48663 + 1.85313i) q^{36} +(0.225314 - 0.130085i) q^{37} -1.95239i q^{38} +(-1.09244 - 6.14871i) q^{39} -9.89813i q^{40} +(-2.92623 + 1.68946i) q^{41} +(2.99538 + 2.89213i) q^{42} +(8.07839 + 4.66406i) q^{43} +(0.419892 - 4.34499i) q^{44} +(-0.379702 - 10.8217i) q^{45} +(2.43829 - 4.22324i) q^{46} +6.20944 q^{47} +(-0.612808 - 0.152736i) q^{48} +(-0.725377 - 1.25639i) q^{49} +(-5.74939 + 3.31941i) q^{50} +(0.295931 + 1.03171i) q^{51} +(1.93545 + 4.33288i) q^{52} +0.712815i q^{53} +(4.20324 + 0.892332i) q^{54} +(-10.8951 + 4.96061i) q^{55} +(-6.90383 - 3.98593i) q^{56} +(1.12750 + 3.93083i) q^{57} +(-4.81652 - 2.78082i) q^{58} +(0.121513 - 0.210467i) q^{59} +(2.26870 + 7.90942i) q^{60} +(-8.04868 - 4.64691i) q^{61} +(2.34440 + 4.06063i) q^{62} +(-7.70091 - 4.09301i) q^{63} -4.05550 q^{64} +(7.63664 - 10.5379i) q^{65} +(-0.864468 - 4.67110i) q^{66} +(-4.43422 + 2.56010i) q^{67} +(-0.407800 - 0.706330i) q^{68} +(-2.47019 + 9.91091i) q^{69} +8.67690i q^{70} +(-7.67720 + 13.2973i) q^{71} +(-8.22177 + 0.288478i) q^{72} +13.2442 q^{73} +(-0.107573 + 0.186322i) q^{74} +(9.65852 - 10.0034i) q^{75} +(-1.55372 - 2.69112i) q^{76} +(-0.927415 + 9.59678i) q^{77} +(3.32466 + 3.95172i) q^{78} -0.316398i q^{79} +(-0.658055 - 1.13979i) q^{80} +(-8.97787 + 0.630791i) q^{81} +(1.39709 - 2.41982i) q^{82} +15.6297i q^{83} +(6.43032 + 1.60269i) q^{84} +(-1.11835 + 1.93704i) q^{85} -7.71382 q^{86} +(11.3032 + 2.81721i) q^{87} +(3.76882 + 8.27750i) q^{88} +(5.29627 + 9.17341i) q^{89} +(4.74639 + 7.59300i) q^{90} +(-4.27484 - 9.57003i) q^{91} -7.76159i q^{92} +(-7.06508 - 6.82153i) q^{93} +(-4.44691 + 2.56742i) q^{94} +(-4.26092 + 7.38013i) q^{95} +(9.63333 - 2.76318i) q^{96} +(12.7818 + 7.37955i) q^{97} +(1.03896 + 0.599844i) q^{98} +(4.43801 + 8.90528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9} - 4 q^{12} - 36 q^{15} - 44 q^{16} - 12 q^{22} + 64 q^{25} + 4 q^{27} + 12 q^{33} + 28 q^{36} - 12 q^{37} + 50 q^{42} - 66 q^{45} + 16 q^{48} - 24 q^{49} - 8 q^{55} - 24 q^{58} - 104 q^{64} - 60 q^{66} - 60 q^{67} - 42 q^{69} - 42 q^{75} + 16 q^{78} - 22 q^{81} - 16 q^{82} + 92 q^{88} - 84 q^{91} + 126 q^{93} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.716153 + 0.413471i −0.506397 + 0.292368i −0.731351 0.682001i \(-0.761110\pi\)
0.224955 + 0.974369i \(0.427777\pi\)
\(3\) 1.20308 1.24603i 0.694599 0.719397i
\(4\) −0.658083 + 1.13983i −0.329042 + 0.569917i
\(5\) 3.60945 1.61420 0.807099 0.590417i \(-0.201037\pi\)
0.807099 + 0.590417i \(0.201037\pi\)
\(6\) −0.346391 + 1.38979i −0.141413 + 0.567379i
\(7\) 1.45351 2.51755i 0.549375 0.951545i −0.448943 0.893561i \(-0.648199\pi\)
0.998317 0.0579844i \(-0.0184674\pi\)
\(8\) 2.74228i 0.969542i
\(9\) −0.105197 2.99816i −0.0350655 0.999385i
\(10\) −2.58492 + 1.49241i −0.817424 + 0.471940i
\(11\) −3.01848 + 1.37434i −0.910105 + 0.414378i
\(12\) 0.628544 + 2.19131i 0.181445 + 0.632575i
\(13\) 2.11573 2.91953i 0.586799 0.809733i
\(14\) 2.40394i 0.642479i
\(15\) 4.34246 4.49750i 1.12122 1.16125i
\(16\) −0.182314 0.315778i −0.0455786 0.0789444i
\(17\) −0.309839 + 0.536657i −0.0751470 + 0.130158i −0.901150 0.433507i \(-0.857276\pi\)
0.826003 + 0.563665i \(0.190609\pi\)
\(18\) 1.31499 + 2.10364i 0.309945 + 0.495833i
\(19\) −1.18049 + 2.04467i −0.270823 + 0.469079i −0.969073 0.246775i \(-0.920629\pi\)
0.698250 + 0.715854i \(0.253962\pi\)
\(20\) −2.37532 + 4.11418i −0.531138 + 0.919958i
\(21\) −1.38826 4.83994i −0.302944 1.05616i
\(22\) 1.59344 2.23229i 0.339723 0.475925i
\(23\) −5.10705 + 2.94856i −1.06489 + 0.614817i −0.926782 0.375600i \(-0.877437\pi\)
−0.138112 + 0.990417i \(0.544103\pi\)
\(24\) −3.41697 3.29918i −0.697486 0.673442i
\(25\) 8.02816 1.60563
\(26\) −0.308046 + 2.96563i −0.0604127 + 0.581607i
\(27\) −3.86236 3.47594i −0.743312 0.668945i
\(28\) 1.91306 + 3.31352i 0.361534 + 0.626196i
\(29\) 3.36278 + 5.82450i 0.624452 + 1.08158i 0.988647 + 0.150259i \(0.0480109\pi\)
−0.364195 + 0.931323i \(0.618656\pi\)
\(30\) −1.25028 + 5.01638i −0.228269 + 0.915862i
\(31\) 5.67006i 1.01837i −0.860656 0.509186i \(-0.829946\pi\)
0.860656 0.509186i \(-0.170054\pi\)
\(32\) 5.01089 + 2.89304i 0.885809 + 0.511422i
\(33\) −1.91900 + 5.41456i −0.334055 + 0.942554i
\(34\) 0.512438i 0.0878824i
\(35\) 5.24637 9.08699i 0.886799 1.53598i
\(36\) 3.48663 + 1.85313i 0.581104 + 0.308855i
\(37\) 0.225314 0.130085i 0.0370414 0.0213859i −0.481365 0.876520i \(-0.659859\pi\)
0.518406 + 0.855134i \(0.326525\pi\)
\(38\) 1.95239i 0.316720i
\(39\) −1.09244 6.14871i −0.174930 0.984581i
\(40\) 9.89813i 1.56503i
\(41\) −2.92623 + 1.68946i −0.457000 + 0.263849i −0.710782 0.703412i \(-0.751659\pi\)
0.253782 + 0.967261i \(0.418325\pi\)
\(42\) 2.99538 + 2.89213i 0.462198 + 0.446265i
\(43\) 8.07839 + 4.66406i 1.23194 + 0.711263i 0.967435 0.253121i \(-0.0814570\pi\)
0.264508 + 0.964383i \(0.414790\pi\)
\(44\) 0.419892 4.34499i 0.0633011 0.655032i
\(45\) −0.379702 10.8217i −0.0566027 1.61320i
\(46\) 2.43829 4.22324i 0.359506 0.622682i
\(47\) 6.20944 0.905740 0.452870 0.891577i \(-0.350400\pi\)
0.452870 + 0.891577i \(0.350400\pi\)
\(48\) −0.612808 0.152736i −0.0884512 0.0220456i
\(49\) −0.725377 1.25639i −0.103625 0.179484i
\(50\) −5.74939 + 3.31941i −0.813087 + 0.469436i
\(51\) 0.295931 + 1.03171i 0.0414387 + 0.144468i
\(52\) 1.93545 + 4.33288i 0.268399 + 0.600862i
\(53\) 0.712815i 0.0979126i 0.998801 + 0.0489563i \(0.0155895\pi\)
−0.998801 + 0.0489563i \(0.984410\pi\)
\(54\) 4.20324 + 0.892332i 0.571989 + 0.121431i
\(55\) −10.8951 + 4.96061i −1.46909 + 0.668889i
\(56\) −6.90383 3.98593i −0.922562 0.532642i
\(57\) 1.12750 + 3.93083i 0.149341 + 0.520651i
\(58\) −4.81652 2.78082i −0.632440 0.365140i
\(59\) 0.121513 0.210467i 0.0158196 0.0274004i −0.858007 0.513638i \(-0.828298\pi\)
0.873827 + 0.486237i \(0.161631\pi\)
\(60\) 2.26870 + 7.90942i 0.292888 + 1.02110i
\(61\) −8.04868 4.64691i −1.03053 0.594975i −0.113392 0.993550i \(-0.536172\pi\)
−0.917136 + 0.398575i \(0.869505\pi\)
\(62\) 2.34440 + 4.06063i 0.297740 + 0.515700i
\(63\) −7.70091 4.09301i −0.970224 0.515670i
\(64\) −4.05550 −0.506937
\(65\) 7.63664 10.5379i 0.947209 1.30707i
\(66\) −0.864468 4.67110i −0.106409 0.574973i
\(67\) −4.43422 + 2.56010i −0.541726 + 0.312765i −0.745778 0.666194i \(-0.767922\pi\)
0.204052 + 0.978960i \(0.434589\pi\)
\(68\) −0.407800 0.706330i −0.0494530 0.0856551i
\(69\) −2.47019 + 9.91091i −0.297376 + 1.19313i
\(70\) 8.67690i 1.03709i
\(71\) −7.67720 + 13.2973i −0.911116 + 1.57810i −0.0986246 + 0.995125i \(0.531444\pi\)
−0.812491 + 0.582974i \(0.801889\pi\)
\(72\) −8.22177 + 0.288478i −0.968945 + 0.0339975i
\(73\) 13.2442 1.55011 0.775057 0.631891i \(-0.217721\pi\)
0.775057 + 0.631891i \(0.217721\pi\)
\(74\) −0.107573 + 0.186322i −0.0125051 + 0.0216595i
\(75\) 9.65852 10.0034i 1.11527 1.15509i
\(76\) −1.55372 2.69112i −0.178224 0.308693i
\(77\) −0.927415 + 9.59678i −0.105689 + 1.09365i
\(78\) 3.32466 + 3.95172i 0.376444 + 0.447444i
\(79\) 0.316398i 0.0355975i −0.999842 0.0177988i \(-0.994334\pi\)
0.999842 0.0177988i \(-0.00566582\pi\)
\(80\) −0.658055 1.13979i −0.0735728 0.127432i
\(81\) −8.97787 + 0.630791i −0.997541 + 0.0700879i
\(82\) 1.39709 2.41982i 0.154282 0.267225i
\(83\) 15.6297i 1.71558i 0.513997 + 0.857792i \(0.328164\pi\)
−0.513997 + 0.857792i \(0.671836\pi\)
\(84\) 6.43032 + 1.60269i 0.701605 + 0.174868i
\(85\) −1.11835 + 1.93704i −0.121302 + 0.210101i
\(86\) −7.71382 −0.831802
\(87\) 11.3032 + 2.81721i 1.21183 + 0.302036i
\(88\) 3.76882 + 8.27750i 0.401757 + 0.882384i
\(89\) 5.29627 + 9.17341i 0.561403 + 0.972379i 0.997374 + 0.0724184i \(0.0230717\pi\)
−0.435971 + 0.899961i \(0.643595\pi\)
\(90\) 4.74639 + 7.59300i 0.500313 + 0.800372i
\(91\) −4.27484 9.57003i −0.448125 1.00321i
\(92\) 7.76159i 0.809202i
\(93\) −7.06508 6.82153i −0.732614 0.707360i
\(94\) −4.44691 + 2.56742i −0.458664 + 0.264810i
\(95\) −4.26092 + 7.38013i −0.437161 + 0.757186i
\(96\) 9.63333 2.76318i 0.983198 0.282016i
\(97\) 12.7818 + 7.37955i 1.29779 + 0.749279i 0.980022 0.198889i \(-0.0637333\pi\)
0.317768 + 0.948168i \(0.397067\pi\)
\(98\) 1.03896 + 0.599844i 0.104951 + 0.0605934i
\(99\) 4.43801 + 8.90528i 0.446037 + 0.895015i
\(100\) −5.28320 + 9.15077i −0.528320 + 0.915077i
\(101\) −7.75309 13.4287i −0.771461 1.33621i −0.936762 0.349967i \(-0.886193\pi\)
0.165301 0.986243i \(-0.447140\pi\)
\(102\) −0.638515 0.616504i −0.0632224 0.0610430i
\(103\) −18.8109 −1.85349 −0.926747 0.375686i \(-0.877407\pi\)
−0.926747 + 0.375686i \(0.877407\pi\)
\(104\) −8.00617 5.80193i −0.785070 0.568926i
\(105\) −5.01088 17.4695i −0.489012 1.70485i
\(106\) −0.294728 0.510484i −0.0286265 0.0495826i
\(107\) −4.77385 8.26856i −0.461506 0.799352i 0.537530 0.843244i \(-0.319357\pi\)
−0.999036 + 0.0438927i \(0.986024\pi\)
\(108\) 6.50375 2.11499i 0.625824 0.203515i
\(109\) −6.66701 −0.638584 −0.319292 0.947656i \(-0.603445\pi\)
−0.319292 + 0.947656i \(0.603445\pi\)
\(110\) 5.75145 8.05734i 0.548380 0.768238i
\(111\) 0.108981 0.437252i 0.0103440 0.0415021i
\(112\) −1.05998 −0.100159
\(113\) −8.81795 5.09105i −0.829523 0.478926i 0.0241661 0.999708i \(-0.492307\pi\)
−0.853689 + 0.520782i \(0.825640\pi\)
\(114\) −2.43274 2.34888i −0.227847 0.219993i
\(115\) −18.4337 + 10.6427i −1.71895 + 0.992436i
\(116\) −8.85195 −0.821883
\(117\) −8.97578 6.03617i −0.829811 0.558044i
\(118\) 0.200968i 0.0185006i
\(119\) 0.900708 + 1.56007i 0.0825678 + 0.143012i
\(120\) −12.3334 11.9082i −1.12588 1.08707i
\(121\) 7.22239 8.29681i 0.656581 0.754256i
\(122\) 7.68544 0.695807
\(123\) −1.41537 + 5.67873i −0.127619 + 0.512034i
\(124\) 6.46292 + 3.73137i 0.580388 + 0.335087i
\(125\) 10.9300 0.977611
\(126\) 7.20737 0.252886i 0.642084 0.0225288i
\(127\) −11.2624 + 6.50233i −0.999373 + 0.576988i −0.908063 0.418834i \(-0.862439\pi\)
−0.0913103 + 0.995822i \(0.529106\pi\)
\(128\) −7.11743 + 4.10925i −0.629098 + 0.363210i
\(129\) 15.5305 4.45470i 1.36739 0.392215i
\(130\) −1.11188 + 10.7043i −0.0975180 + 0.938829i
\(131\) −1.19424 −0.104341 −0.0521706 0.998638i \(-0.516614\pi\)
−0.0521706 + 0.998638i \(0.516614\pi\)
\(132\) −4.90884 5.75057i −0.427259 0.500523i
\(133\) 3.43170 + 5.94388i 0.297566 + 0.515400i
\(134\) 2.11705 3.66684i 0.182885 0.316767i
\(135\) −13.9410 12.5463i −1.19985 1.07981i
\(136\) 1.47166 + 0.849665i 0.126194 + 0.0728582i
\(137\) −0.795650 + 1.37811i −0.0679769 + 0.117740i −0.898011 0.439974i \(-0.854988\pi\)
0.830034 + 0.557713i \(0.188321\pi\)
\(138\) −2.32884 8.11908i −0.198244 0.691142i
\(139\) −6.24093 3.60320i −0.529349 0.305620i 0.211402 0.977399i \(-0.432197\pi\)
−0.740751 + 0.671779i \(0.765530\pi\)
\(140\) 6.90510 + 11.9600i 0.583588 + 1.01080i
\(141\) 7.47045 7.73717i 0.629126 0.651587i
\(142\) 12.6972i 1.06552i
\(143\) −2.37386 + 11.7203i −0.198512 + 0.980098i
\(144\) −0.927571 + 0.579825i −0.0772976 + 0.0483188i
\(145\) 12.1378 + 21.0233i 1.00799 + 1.74589i
\(146\) −9.48486 + 5.47609i −0.784972 + 0.453204i
\(147\) −2.43819 0.607694i −0.201098 0.0501217i
\(148\) 0.342428i 0.0281474i
\(149\) −0.645717 0.372805i −0.0528992 0.0305414i 0.473317 0.880892i \(-0.343056\pi\)
−0.526216 + 0.850351i \(0.676390\pi\)
\(150\) −2.78088 + 11.1575i −0.227058 + 0.911002i
\(151\) 5.46182 0.444477 0.222238 0.974992i \(-0.428664\pi\)
0.222238 + 0.974992i \(0.428664\pi\)
\(152\) 5.60704 + 3.23723i 0.454791 + 0.262574i
\(153\) 1.64158 + 0.872491i 0.132714 + 0.0705367i
\(154\) −3.30382 7.25622i −0.266229 0.584723i
\(155\) 20.4658i 1.64385i
\(156\) 7.72742 + 2.80116i 0.618689 + 0.224272i
\(157\) 8.52908 0.680695 0.340347 0.940300i \(-0.389455\pi\)
0.340347 + 0.940300i \(0.389455\pi\)
\(158\) 0.130821 + 0.226589i 0.0104076 + 0.0180265i
\(159\) 0.888191 + 0.857573i 0.0704381 + 0.0680100i
\(160\) 18.0866 + 10.4423i 1.42987 + 0.825536i
\(161\) 17.1430i 1.35106i
\(162\) 6.16871 4.16383i 0.484660 0.327141i
\(163\) −11.4306 6.59946i −0.895314 0.516910i −0.0196371 0.999807i \(-0.506251\pi\)
−0.875677 + 0.482897i \(0.839584\pi\)
\(164\) 4.44722i 0.347270i
\(165\) −6.92653 + 19.5436i −0.539230 + 1.52147i
\(166\) −6.46243 11.1933i −0.501582 0.868766i
\(167\) 18.4673 10.6621i 1.42904 0.825057i 0.431996 0.901876i \(-0.357810\pi\)
0.997045 + 0.0768186i \(0.0244762\pi\)
\(168\) −13.2724 + 3.80701i −1.02399 + 0.293717i
\(169\) −4.04735 12.3539i −0.311335 0.950300i
\(170\) 1.84962i 0.141860i
\(171\) 6.25441 + 3.32420i 0.478287 + 0.254208i
\(172\) −10.6325 + 6.13868i −0.810721 + 0.468070i
\(173\) 5.03566 8.72202i 0.382854 0.663123i −0.608615 0.793466i \(-0.708275\pi\)
0.991469 + 0.130343i \(0.0416078\pi\)
\(174\) −9.25966 + 2.65600i −0.701973 + 0.201351i
\(175\) 11.6690 20.2113i 0.882094 1.52783i
\(176\) 0.984296 + 0.702606i 0.0741941 + 0.0529609i
\(177\) −0.116059 0.404618i −0.00872350 0.0304129i
\(178\) −7.58588 4.37971i −0.568585 0.328273i
\(179\) 9.04701 5.22330i 0.676205 0.390407i −0.122218 0.992503i \(-0.539001\pi\)
0.798424 + 0.602096i \(0.205667\pi\)
\(180\) 12.5848 + 6.68879i 0.938017 + 0.498553i
\(181\) 17.7170 1.31690 0.658448 0.752626i \(-0.271213\pi\)
0.658448 + 0.752626i \(0.271213\pi\)
\(182\) 7.01837 + 5.08608i 0.520236 + 0.377006i
\(183\) −15.4734 + 4.43832i −1.14383 + 0.328090i
\(184\) 8.08577 + 14.0050i 0.596091 + 1.03246i
\(185\) 0.813261 0.469537i 0.0597922 0.0345210i
\(186\) 7.88018 + 1.96405i 0.577803 + 0.144011i
\(187\) 0.197694 2.04571i 0.0144568 0.149597i
\(188\) −4.08633 + 7.07773i −0.298026 + 0.516197i
\(189\) −14.3648 + 4.67138i −1.04489 + 0.339793i
\(190\) 7.04707i 0.511248i
\(191\) −3.82809 2.21015i −0.276991 0.159921i 0.355070 0.934840i \(-0.384457\pi\)
−0.632060 + 0.774919i \(0.717791\pi\)
\(192\) −4.87909 + 5.05328i −0.352118 + 0.364689i
\(193\) 0.123929 + 0.214651i 0.00892061 + 0.0154509i 0.870451 0.492255i \(-0.163827\pi\)
−0.861531 + 0.507706i \(0.830494\pi\)
\(194\) −12.2049 −0.876262
\(195\) −3.94311 22.1935i −0.282372 1.58931i
\(196\) 1.90943 0.136388
\(197\) −3.20326 + 1.84940i −0.228223 + 0.131765i −0.609752 0.792592i \(-0.708731\pi\)
0.381529 + 0.924357i \(0.375398\pi\)
\(198\) −6.86037 4.54255i −0.487545 0.322825i
\(199\) 2.15254 3.72831i 0.152590 0.264293i −0.779589 0.626291i \(-0.784572\pi\)
0.932179 + 0.361998i \(0.117905\pi\)
\(200\) 22.0155i 1.55673i
\(201\) −2.14475 + 8.60518i −0.151279 + 0.606963i
\(202\) 11.1048 + 6.41136i 0.781331 + 0.451101i
\(203\) 19.5513 1.37223
\(204\) −1.37073 0.341640i −0.0959701 0.0239196i
\(205\) −10.5621 + 6.09803i −0.737689 + 0.425905i
\(206\) 13.4715 7.77777i 0.938603 0.541903i
\(207\) 9.37748 + 15.0016i 0.651780 + 1.04268i
\(208\) −1.30765 0.135828i −0.0906693 0.00941800i
\(209\) 0.753214 7.79417i 0.0521009 0.539134i
\(210\) 10.8117 + 10.4390i 0.746078 + 0.720360i
\(211\) −11.2825 + 6.51393i −0.776716 + 0.448437i −0.835265 0.549847i \(-0.814686\pi\)
0.0585490 + 0.998285i \(0.481353\pi\)
\(212\) −0.812490 0.469092i −0.0558021 0.0322173i
\(213\) 7.33259 + 25.5638i 0.502420 + 1.75160i
\(214\) 6.83762 + 3.94770i 0.467410 + 0.269859i
\(215\) 29.1586 + 16.8347i 1.98860 + 1.14812i
\(216\) −9.53200 + 10.5917i −0.648570 + 0.720671i
\(217\) −14.2747 8.24148i −0.969027 0.559468i
\(218\) 4.77460 2.75662i 0.323377 0.186702i
\(219\) 15.9338 16.5027i 1.07671 1.11515i
\(220\) 1.51558 15.6830i 0.102180 1.05735i
\(221\) 0.911252 + 2.04001i 0.0612974 + 0.137226i
\(222\) 0.102744 + 0.358199i 0.00689574 + 0.0240408i
\(223\) −3.59489 + 2.07551i −0.240732 + 0.138987i −0.615513 0.788127i \(-0.711051\pi\)
0.374781 + 0.927113i \(0.377718\pi\)
\(224\) 14.5668 8.41012i 0.973283 0.561925i
\(225\) −0.844535 24.0697i −0.0563023 1.60465i
\(226\) 8.42000 0.560090
\(227\) −7.31729 4.22464i −0.485665 0.280399i 0.237109 0.971483i \(-0.423800\pi\)
−0.722774 + 0.691084i \(0.757133\pi\)
\(228\) −5.22248 1.30165i −0.345867 0.0862038i
\(229\) 15.9604i 1.05469i −0.849650 0.527346i \(-0.823187\pi\)
0.849650 0.527346i \(-0.176813\pi\)
\(230\) 8.80089 15.2436i 0.580313 1.00513i
\(231\) 10.8422 + 12.7013i 0.713361 + 0.835683i
\(232\) 15.9724 9.22167i 1.04864 0.605432i
\(233\) −14.4909 −0.949331 −0.474666 0.880166i \(-0.657431\pi\)
−0.474666 + 0.880166i \(0.657431\pi\)
\(234\) 8.92381 + 0.611595i 0.583368 + 0.0399812i
\(235\) 22.4127 1.46204
\(236\) 0.159931 + 0.277009i 0.0104106 + 0.0180318i
\(237\) −0.394242 0.380652i −0.0256088 0.0247260i
\(238\) −1.29009 0.744833i −0.0836241 0.0482804i
\(239\) 0.504548i 0.0326365i 0.999867 + 0.0163182i \(0.00519449\pi\)
−0.999867 + 0.0163182i \(0.994806\pi\)
\(240\) −2.21190 0.551294i −0.142778 0.0355859i
\(241\) −9.18385 + 15.9069i −0.591584 + 1.02465i 0.402435 + 0.915448i \(0.368164\pi\)
−0.994019 + 0.109205i \(0.965169\pi\)
\(242\) −1.74184 + 8.92803i −0.111970 + 0.573916i
\(243\) −10.0151 + 11.9456i −0.642469 + 0.766311i
\(244\) 10.5934 6.11610i 0.678173 0.391543i
\(245\) −2.61821 4.53488i −0.167272 0.289723i
\(246\) −1.33437 4.65205i −0.0850765 0.296604i
\(247\) 3.47187 + 7.77244i 0.220910 + 0.494549i
\(248\) −15.5489 −0.987354
\(249\) 19.4751 + 18.8038i 1.23419 + 1.19164i
\(250\) −7.82756 + 4.51925i −0.495059 + 0.285822i
\(251\) 10.8243 + 6.24940i 0.683222 + 0.394459i 0.801068 0.598573i \(-0.204265\pi\)
−0.117846 + 0.993032i \(0.537599\pi\)
\(252\) 9.73319 6.08422i 0.613133 0.383270i
\(253\) 11.3632 15.9190i 0.714398 1.00082i
\(254\) 5.37705 9.31332i 0.337386 0.584370i
\(255\) 1.06815 + 3.72392i 0.0668902 + 0.233201i
\(256\) 7.45361 12.9100i 0.465851 0.806877i
\(257\) 8.57172 4.94889i 0.534689 0.308703i −0.208235 0.978079i \(-0.566772\pi\)
0.742924 + 0.669376i \(0.233438\pi\)
\(258\) −9.28034 + 9.61167i −0.577769 + 0.598396i
\(259\) 0.756320i 0.0469954i
\(260\) 6.98594 + 15.6393i 0.433249 + 0.969910i
\(261\) 17.1090 10.6948i 1.05902 0.661994i
\(262\) 0.855258 0.493783i 0.0528380 0.0305060i
\(263\) −5.57568 9.65736i −0.343811 0.595498i 0.641326 0.767269i \(-0.278385\pi\)
−0.985137 + 0.171770i \(0.945051\pi\)
\(264\) 14.8482 + 5.26242i 0.913845 + 0.323880i
\(265\) 2.57287i 0.158050i
\(266\) −4.91525 2.83782i −0.301373 0.173998i
\(267\) 17.8022 + 4.43702i 1.08948 + 0.271541i
\(268\) 6.73903i 0.411652i
\(269\) −0.197250 0.113882i −0.0120266 0.00694353i 0.493975 0.869476i \(-0.335544\pi\)
−0.506001 + 0.862533i \(0.668877\pi\)
\(270\) 15.1714 + 3.22083i 0.923303 + 0.196014i
\(271\) −2.56137 4.43643i −0.155592 0.269494i 0.777682 0.628658i \(-0.216395\pi\)
−0.933275 + 0.359164i \(0.883062\pi\)
\(272\) 0.225952 0.0137004
\(273\) −17.0676 6.18693i −1.03298 0.374450i
\(274\) 1.31591i 0.0794972i
\(275\) −24.2328 + 11.0334i −1.46129 + 0.665340i
\(276\) −9.67120 9.33781i −0.582138 0.562070i
\(277\) 0.815907 + 0.471064i 0.0490231 + 0.0283035i 0.524311 0.851527i \(-0.324323\pi\)
−0.475288 + 0.879830i \(0.657656\pi\)
\(278\) 5.95928 0.357414
\(279\) −16.9997 + 0.596470i −1.01775 + 0.0357097i
\(280\) −24.9190 14.3870i −1.48920 0.859789i
\(281\) 17.7047i 1.05618i 0.849190 + 0.528088i \(0.177091\pi\)
−0.849190 + 0.528088i \(0.822909\pi\)
\(282\) −2.15089 + 8.62981i −0.128084 + 0.513898i
\(283\) −4.13971 + 2.39006i −0.246080 + 0.142075i −0.617968 0.786203i \(-0.712044\pi\)
0.371888 + 0.928278i \(0.378711\pi\)
\(284\) −10.1045 17.5015i −0.599590 1.03852i
\(285\) 4.06966 + 14.1881i 0.241066 + 0.840433i
\(286\) −3.14594 9.37503i −0.186024 0.554357i
\(287\) 9.82258i 0.579808i
\(288\) 8.14666 15.3278i 0.480046 0.903198i
\(289\) 8.30800 + 14.3899i 0.488706 + 0.846463i
\(290\) −17.3850 10.0372i −1.02088 0.589407i
\(291\) 24.5726 7.04830i 1.44047 0.413178i
\(292\) −8.71578 + 15.0962i −0.510052 + 0.883436i
\(293\) −14.7021 8.48825i −0.858905 0.495889i 0.00474047 0.999989i \(-0.498491\pi\)
−0.863645 + 0.504100i \(0.831824\pi\)
\(294\) 1.99738 0.572919i 0.116490 0.0334133i
\(295\) 0.438596 0.759670i 0.0255360 0.0442297i
\(296\) −0.356730 0.617874i −0.0207345 0.0359132i
\(297\) 16.4356 + 5.18386i 0.953688 + 0.300798i
\(298\) 0.616576 0.0357173
\(299\) −2.19674 + 21.1486i −0.127041 + 1.22305i
\(300\) 5.04605 + 17.5922i 0.291334 + 1.01568i
\(301\) 23.4840 13.5585i 1.35360 0.781499i
\(302\) −3.91150 + 2.25831i −0.225082 + 0.129951i
\(303\) −26.0602 6.49525i −1.49712 0.373142i
\(304\) 0.860880 0.0493749
\(305\) −29.0513 16.7728i −1.66347 0.960408i
\(306\) −1.53637 + 0.0539067i −0.0878284 + 0.00308164i
\(307\) 26.7631 1.52745 0.763725 0.645542i \(-0.223368\pi\)
0.763725 + 0.645542i \(0.223368\pi\)
\(308\) −10.3284 7.37258i −0.588516 0.420092i
\(309\) −22.6310 + 23.4390i −1.28743 + 1.33340i
\(310\) 8.46202 + 14.6566i 0.480610 + 0.832442i
\(311\) 0.437159i 0.0247890i 0.999923 + 0.0123945i \(0.00394539\pi\)
−0.999923 + 0.0123945i \(0.996055\pi\)
\(312\) −16.8615 + 2.99577i −0.954592 + 0.169602i
\(313\) −14.0254 −0.792764 −0.396382 0.918086i \(-0.629734\pi\)
−0.396382 + 0.918086i \(0.629734\pi\)
\(314\) −6.10813 + 3.52653i −0.344701 + 0.199014i
\(315\) −27.7961 14.7735i −1.56613 0.832394i
\(316\) 0.360641 + 0.208216i 0.0202876 + 0.0117131i
\(317\) −1.32272 −0.0742914 −0.0371457 0.999310i \(-0.511827\pi\)
−0.0371457 + 0.999310i \(0.511827\pi\)
\(318\) −0.990662 0.246912i −0.0555536 0.0138462i
\(319\) −18.1553 12.9595i −1.01650 0.725594i
\(320\) −14.6381 −0.818297
\(321\) −16.0462 3.99936i −0.895613 0.223222i
\(322\) −7.08814 12.2770i −0.395007 0.684172i
\(323\) −0.731523 1.26704i −0.0407030 0.0704997i
\(324\) 5.18919 10.6484i 0.288288 0.591577i
\(325\) 16.9854 23.4385i 0.942183 1.30013i
\(326\) 10.9147 0.604512
\(327\) −8.02095 + 8.30731i −0.443559 + 0.459396i
\(328\) 4.63297 + 8.02453i 0.255813 + 0.443081i
\(329\) 9.02548 15.6326i 0.497591 0.861852i
\(330\) −3.12026 16.8601i −0.171765 0.928120i
\(331\) −19.4419 11.2248i −1.06862 0.616971i −0.140819 0.990035i \(-0.544974\pi\)
−0.927805 + 0.373064i \(0.878307\pi\)
\(332\) −17.8153 10.2857i −0.977740 0.564498i
\(333\) −0.413718 0.661842i −0.0226716 0.0362687i
\(334\) −8.81693 + 15.2714i −0.482441 + 0.835612i
\(335\) −16.0051 + 9.24055i −0.874452 + 0.504865i
\(336\) −1.27524 + 1.32077i −0.0695702 + 0.0720540i
\(337\) 14.1245i 0.769412i −0.923039 0.384706i \(-0.874303\pi\)
0.923039 0.384706i \(-0.125697\pi\)
\(338\) 8.00650 + 7.17382i 0.435496 + 0.390204i
\(339\) −16.9523 + 4.86252i −0.920724 + 0.264096i
\(340\) −1.47194 2.54947i −0.0798269 0.138264i
\(341\) 7.79257 + 17.1149i 0.421992 + 0.926825i
\(342\) −5.85357 + 0.205385i −0.316525 + 0.0111059i
\(343\) 16.1318 0.871033
\(344\) 12.7902 22.1532i 0.689599 1.19442i
\(345\) −8.91605 + 35.7730i −0.480024 + 1.92595i
\(346\) 8.32840i 0.447737i
\(347\) 11.7907 20.4220i 0.632955 1.09631i −0.353989 0.935250i \(-0.615175\pi\)
0.986944 0.161061i \(-0.0514917\pi\)
\(348\) −10.6496 + 11.0298i −0.570879 + 0.591260i
\(349\) 12.2094 + 21.1474i 0.653556 + 1.13199i 0.982254 + 0.187557i \(0.0600571\pi\)
−0.328697 + 0.944435i \(0.606610\pi\)
\(350\) 19.2992i 1.03158i
\(351\) −18.3199 + 3.92212i −0.977841 + 0.209347i
\(352\) −19.1013 1.84591i −1.01810 0.0983874i
\(353\) −4.65200 8.05750i −0.247601 0.428857i 0.715259 0.698860i \(-0.246309\pi\)
−0.962860 + 0.270002i \(0.912976\pi\)
\(354\) 0.250413 + 0.241781i 0.0133093 + 0.0128505i
\(355\) −27.7105 + 47.9960i −1.47072 + 2.54736i
\(356\) −13.9415 −0.738900
\(357\) 3.02753 + 0.754580i 0.160234 + 0.0399366i
\(358\) −4.31936 + 7.48136i −0.228285 + 0.395402i
\(359\) 5.02549i 0.265235i −0.991167 0.132618i \(-0.957662\pi\)
0.991167 0.132618i \(-0.0423382\pi\)
\(360\) −29.6761 + 1.04125i −1.56407 + 0.0548786i
\(361\) 6.71289 + 11.6271i 0.353310 + 0.611951i
\(362\) −12.6881 + 7.32548i −0.666872 + 0.385019i
\(363\) −1.64899 18.9811i −0.0865494 0.996248i
\(364\) 13.7214 + 1.42527i 0.719199 + 0.0747047i
\(365\) 47.8043 2.50219
\(366\) 9.24621 9.57632i 0.483307 0.500562i
\(367\) −10.9474 18.9615i −0.571451 0.989782i −0.996417 0.0845732i \(-0.973047\pi\)
0.424966 0.905209i \(-0.360286\pi\)
\(368\) 1.86218 + 1.07513i 0.0970727 + 0.0560450i
\(369\) 5.37309 + 8.59556i 0.279712 + 0.447467i
\(370\) −0.388280 + 0.672520i −0.0201857 + 0.0349627i
\(371\) 1.79455 + 1.03608i 0.0931683 + 0.0537907i
\(372\) 12.4248 3.56388i 0.644197 0.184778i
\(373\) −17.6888 10.2126i −0.915890 0.528789i −0.0335684 0.999436i \(-0.510687\pi\)
−0.882322 + 0.470647i \(0.844021\pi\)
\(374\) 0.704263 + 1.54678i 0.0364166 + 0.0799822i
\(375\) 13.1497 13.6192i 0.679047 0.703291i
\(376\) 17.0280i 0.878153i
\(377\) 24.1196 + 2.50535i 1.24222 + 0.129032i
\(378\) 8.35594 9.28486i 0.429783 0.477562i
\(379\) −2.07421 + 1.19754i −0.106545 + 0.0615137i −0.552326 0.833629i \(-0.686259\pi\)
0.445781 + 0.895142i \(0.352926\pi\)
\(380\) −5.60808 9.71348i −0.287689 0.498291i
\(381\) −5.44741 + 21.8561i −0.279079 + 1.11972i
\(382\) 3.65533 0.187023
\(383\) 4.75807 8.24123i 0.243126 0.421107i −0.718477 0.695551i \(-0.755160\pi\)
0.961603 + 0.274444i \(0.0884937\pi\)
\(384\) −3.44258 + 13.8123i −0.175678 + 0.704857i
\(385\) −3.34746 + 34.6391i −0.170602 + 1.76537i
\(386\) −0.177504 0.102482i −0.00903473 0.00521620i
\(387\) 13.1338 24.7109i 0.667626 1.25613i
\(388\) −16.8229 + 9.71271i −0.854054 + 0.493088i
\(389\) 10.2200i 0.518174i 0.965854 + 0.259087i \(0.0834216\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(390\) 12.0002 + 14.2636i 0.607655 + 0.722263i
\(391\) 3.65432i 0.184807i
\(392\) −3.44537 + 1.98918i −0.174017 + 0.100469i
\(393\) −1.43677 + 1.48806i −0.0724752 + 0.0750628i
\(394\) 1.52935 2.64891i 0.0770476 0.133450i
\(395\) 1.14202i 0.0574614i
\(396\) −13.0711 0.801823i −0.656849 0.0402931i
\(397\) 25.4773 + 14.7093i 1.27867 + 0.738239i 0.976603 0.215049i \(-0.0689912\pi\)
0.302063 + 0.953288i \(0.402325\pi\)
\(398\) 3.56005i 0.178449i
\(399\) 11.5349 + 2.87495i 0.577467 + 0.143928i
\(400\) −1.46365 2.53511i −0.0731824 0.126756i
\(401\) −9.74398 16.8771i −0.486591 0.842801i 0.513290 0.858215i \(-0.328427\pi\)
−0.999881 + 0.0154145i \(0.995093\pi\)
\(402\) −2.02202 7.04942i −0.100849 0.351593i
\(403\) −16.5539 11.9963i −0.824609 0.597579i
\(404\) 20.4087 1.01537
\(405\) −32.4052 + 2.27681i −1.61023 + 0.113136i
\(406\) −14.0017 + 8.08390i −0.694894 + 0.401197i
\(407\) −0.501324 + 0.702317i −0.0248497 + 0.0348126i
\(408\) 2.82924 0.811526i 0.140068 0.0401765i
\(409\) 13.6097 23.5727i 0.672956 1.16559i −0.304105 0.952638i \(-0.598357\pi\)
0.977062 0.212956i \(-0.0683092\pi\)
\(410\) 5.04272 8.73424i 0.249042 0.431353i
\(411\) 0.759935 + 2.64938i 0.0374848 + 0.130684i
\(412\) 12.3791 21.4413i 0.609877 1.05634i
\(413\) −0.353240 0.611830i −0.0173818 0.0301062i
\(414\) −12.9184 6.86609i −0.634906 0.337450i
\(415\) 56.4147i 2.76929i
\(416\) 19.0480 8.50857i 0.933907 0.417167i
\(417\) −11.9981 + 3.44147i −0.587547 + 0.168529i
\(418\) 2.68325 + 5.89325i 0.131242 + 0.288248i
\(419\) 19.6051 11.3190i 0.957771 0.552969i 0.0622847 0.998058i \(-0.480161\pi\)
0.895486 + 0.445089i \(0.146828\pi\)
\(420\) 23.2099 + 5.78484i 1.13253 + 0.282271i
\(421\) 16.3608i 0.797379i 0.917086 + 0.398689i \(0.130535\pi\)
−0.917086 + 0.398689i \(0.869465\pi\)
\(422\) 5.38664 9.32994i 0.262218 0.454174i
\(423\) −0.653212 18.6169i −0.0317602 0.905183i
\(424\) 1.95474 0.0949304
\(425\) −2.48744 + 4.30837i −0.120659 + 0.208987i
\(426\) −15.8211 15.2757i −0.766536 0.740112i
\(427\) −23.3977 + 13.5086i −1.13229 + 0.653729i
\(428\) 12.5664 0.607419
\(429\) 11.7479 + 17.0583i 0.567194 + 0.823584i
\(430\) −27.8427 −1.34269
\(431\) −2.91467 + 1.68278i −0.140395 + 0.0810568i −0.568552 0.822647i \(-0.692496\pi\)
0.428157 + 0.903704i \(0.359163\pi\)
\(432\) −0.393461 + 1.85336i −0.0189304 + 0.0891699i
\(433\) −17.9077 + 31.0170i −0.860587 + 1.49058i 0.0107758 + 0.999942i \(0.496570\pi\)
−0.871363 + 0.490639i \(0.836763\pi\)
\(434\) 13.6304 0.654283
\(435\) 40.7984 + 10.1686i 1.95613 + 0.487546i
\(436\) 4.38745 7.59928i 0.210121 0.363940i
\(437\) 13.9230i 0.666026i
\(438\) −4.58766 + 18.4066i −0.219207 + 0.879502i
\(439\) 27.7633 16.0291i 1.32507 0.765029i 0.340537 0.940231i \(-0.389391\pi\)
0.984532 + 0.175202i \(0.0560580\pi\)
\(440\) 13.6034 + 29.8773i 0.648515 + 1.42434i
\(441\) −3.69054 + 2.30696i −0.175740 + 0.109855i
\(442\) −1.49608 1.08418i −0.0711613 0.0515693i
\(443\) 16.7830i 0.797385i −0.917085 0.398693i \(-0.869464\pi\)
0.917085 0.398693i \(-0.130536\pi\)
\(444\) 0.426676 + 0.411968i 0.0202492 + 0.0195511i
\(445\) 19.1166 + 33.1110i 0.906216 + 1.56961i
\(446\) 1.71633 2.97277i 0.0812705 0.140765i
\(447\) −1.24138 + 0.356070i −0.0587151 + 0.0168416i
\(448\) −5.89470 + 10.2099i −0.278499 + 0.482374i
\(449\) −2.77452 + 4.80562i −0.130938 + 0.226791i −0.924038 0.382300i \(-0.875132\pi\)
0.793101 + 0.609091i \(0.208466\pi\)
\(450\) 10.5569 + 16.8884i 0.497659 + 0.796126i
\(451\) 6.51086 9.12122i 0.306585 0.429501i
\(452\) 11.6059 6.70067i 0.545896 0.315173i
\(453\) 6.57101 6.80561i 0.308733 0.319756i
\(454\) 6.98706 0.327919
\(455\) −15.4298 34.5426i −0.723362 1.61938i
\(456\) 10.7794 3.09192i 0.504792 0.144792i
\(457\) 9.72010 + 16.8357i 0.454687 + 0.787541i 0.998670 0.0515551i \(-0.0164178\pi\)
−0.543983 + 0.839096i \(0.683084\pi\)
\(458\) 6.59916 + 11.4301i 0.308359 + 0.534093i
\(459\) 3.06210 0.995780i 0.142927 0.0464790i
\(460\) 28.0151i 1.30621i
\(461\) −3.66287 2.11476i −0.170597 0.0984940i 0.412270 0.911061i \(-0.364736\pi\)
−0.582867 + 0.812567i \(0.698069\pi\)
\(462\) −13.0163 4.61315i −0.605571 0.214623i
\(463\) 1.28884i 0.0598974i −0.999551 0.0299487i \(-0.990466\pi\)
0.999551 0.0299487i \(-0.00953439\pi\)
\(464\) 1.22616 2.12378i 0.0569232 0.0985939i
\(465\) −25.5011 24.6220i −1.18258 1.14182i
\(466\) 10.3777 5.99157i 0.480738 0.277554i
\(467\) 7.43668i 0.344128i 0.985086 + 0.172064i \(0.0550437\pi\)
−0.985086 + 0.172064i \(0.944956\pi\)
\(468\) 12.7870 6.25860i 0.591081 0.289304i
\(469\) 14.8845i 0.687302i
\(470\) −16.0509 + 9.26700i −0.740374 + 0.427455i
\(471\) 10.2612 10.6275i 0.472810 0.489690i
\(472\) −0.577158 0.333222i −0.0265659 0.0153378i
\(473\) −30.7944 2.97592i −1.41593 0.136833i
\(474\) 0.439726 + 0.109597i 0.0201973 + 0.00503397i
\(475\) −9.47716 + 16.4149i −0.434842 + 0.753168i
\(476\) −2.37096 −0.108673
\(477\) 2.13713 0.0749856i 0.0978524 0.00343336i
\(478\) −0.208616 0.361333i −0.00954186 0.0165270i
\(479\) −7.29276 + 4.21048i −0.333215 + 0.192382i −0.657267 0.753657i \(-0.728288\pi\)
0.324053 + 0.946039i \(0.394954\pi\)
\(480\) 34.7711 9.97357i 1.58708 0.455229i
\(481\) 0.0969165 0.933038i 0.00441901 0.0425429i
\(482\) 15.1890i 0.691841i
\(483\) 21.3608 + 20.6244i 0.971949 + 0.938444i
\(484\) 4.70405 + 13.6923i 0.213821 + 0.622378i
\(485\) 46.1352 + 26.6361i 2.09489 + 1.20948i
\(486\) 2.23318 12.6958i 0.101299 0.575895i
\(487\) 4.64583 + 2.68227i 0.210523 + 0.121545i 0.601554 0.798832i \(-0.294548\pi\)
−0.391032 + 0.920377i \(0.627882\pi\)
\(488\) −12.7431 + 22.0717i −0.576853 + 0.999139i
\(489\) −21.9751 + 6.30323i −0.993747 + 0.285042i
\(490\) 3.75008 + 2.16511i 0.169411 + 0.0978098i
\(491\) −17.1649 29.7305i −0.774642 1.34172i −0.934996 0.354659i \(-0.884597\pi\)
0.160354 0.987060i \(-0.448736\pi\)
\(492\) −5.54138 5.35036i −0.249825 0.241213i
\(493\) −4.16768 −0.187703
\(494\) −5.70007 4.13074i −0.256458 0.185851i
\(495\) 16.0188 + 32.1432i 0.719992 + 1.44473i
\(496\) −1.79048 + 1.03373i −0.0803948 + 0.0464160i
\(497\) 22.3177 + 38.6555i 1.00109 + 1.73393i
\(498\) −21.7220 5.41399i −0.973386 0.242606i
\(499\) 9.37911i 0.419867i −0.977716 0.209933i \(-0.932675\pi\)
0.977716 0.209933i \(-0.0673247\pi\)
\(500\) −7.19286 + 12.4584i −0.321675 + 0.557157i
\(501\) 8.93230 35.8382i 0.399066 1.60113i
\(502\) −10.3358 −0.461309
\(503\) 6.38729 11.0631i 0.284795 0.493280i −0.687764 0.725934i \(-0.741408\pi\)
0.972560 + 0.232654i \(0.0747411\pi\)
\(504\) −11.2242 + 21.1180i −0.499964 + 0.940672i
\(505\) −27.9844 48.4704i −1.24529 2.15691i
\(506\) −1.55575 + 16.0988i −0.0691617 + 0.715678i
\(507\) −20.2627 9.81961i −0.899896 0.436104i
\(508\) 17.1163i 0.759413i
\(509\) 9.99651 + 17.3145i 0.443088 + 0.767450i 0.997917 0.0645139i \(-0.0205497\pi\)
−0.554829 + 0.831964i \(0.687216\pi\)
\(510\) −2.30469 2.22524i −0.102053 0.0985354i
\(511\) 19.2505 33.3429i 0.851594 1.47500i
\(512\) 4.10960i 0.181620i
\(513\) 11.6666 3.79393i 0.515094 0.167506i
\(514\) −4.09244 + 7.08832i −0.180510 + 0.312652i
\(515\) −67.8971 −2.99191
\(516\) −5.14276 + 20.6338i −0.226397 + 0.908352i
\(517\) −18.7430 + 8.53387i −0.824318 + 0.375319i
\(518\) 0.312716 + 0.541641i 0.0137400 + 0.0237983i
\(519\) −4.80962 16.7679i −0.211119 0.736029i
\(520\) −28.8979 20.9418i −1.26726 0.918358i
\(521\) 24.6791i 1.08121i 0.841276 + 0.540606i \(0.181805\pi\)
−0.841276 + 0.540606i \(0.818195\pi\)
\(522\) −7.83065 + 14.7332i −0.342738 + 0.644855i
\(523\) −16.7524 + 9.67202i −0.732533 + 0.422928i −0.819348 0.573296i \(-0.805664\pi\)
0.0868151 + 0.996224i \(0.472331\pi\)
\(524\) 0.785909 1.36123i 0.0343326 0.0594658i
\(525\) −11.1452 38.8558i −0.486417 1.69581i
\(526\) 7.98608 + 4.61076i 0.348210 + 0.201039i
\(527\) 3.04288 + 1.75681i 0.132550 + 0.0765277i
\(528\) 2.05966 0.381175i 0.0896351 0.0165885i
\(529\) 5.88799 10.1983i 0.256000 0.443404i
\(530\) −1.06381 1.84257i −0.0462089 0.0800361i
\(531\) −0.643795 0.342174i −0.0279383 0.0148491i
\(532\) −9.03338 −0.391647
\(533\) −1.25869 + 12.1177i −0.0545198 + 0.524875i
\(534\) −14.5837 + 4.18311i −0.631097 + 0.181021i
\(535\) −17.2310 29.8450i −0.744962 1.29031i
\(536\) 7.02049 + 12.1599i 0.303239 + 0.525226i
\(537\) 4.37588 17.5569i 0.188833 0.757637i
\(538\) 0.188348 0.00812027
\(539\) 3.91623 + 2.79547i 0.168684 + 0.120409i
\(540\) 23.4750 7.63396i 1.01020 0.328513i
\(541\) −3.98233 −0.171214 −0.0856068 0.996329i \(-0.527283\pi\)
−0.0856068 + 0.996329i \(0.527283\pi\)
\(542\) 3.66867 + 2.11811i 0.157583 + 0.0909805i
\(543\) 21.3150 22.0760i 0.914715 0.947372i
\(544\) −3.10514 + 1.79275i −0.133132 + 0.0768637i
\(545\) −24.0643 −1.03080
\(546\) 14.7811 2.62615i 0.632572 0.112389i
\(547\) 15.7154i 0.671940i 0.941873 + 0.335970i \(0.109064\pi\)
−0.941873 + 0.335970i \(0.890936\pi\)
\(548\) −1.04721 1.81382i −0.0447345 0.0774824i
\(549\) −13.0855 + 24.6200i −0.558474 + 1.05076i
\(550\) 12.7924 17.9212i 0.545470 0.764162i
\(551\) −15.8789 −0.676463
\(552\) 27.1785 + 6.77395i 1.15679 + 0.288319i
\(553\) −0.796547 0.459887i −0.0338726 0.0195564i
\(554\) −0.779086 −0.0331002
\(555\) 0.393360 1.57824i 0.0166972 0.0669926i
\(556\) 8.21411 4.74242i 0.348356 0.201123i
\(557\) 1.76818 1.02086i 0.0749202 0.0432552i −0.462072 0.886842i \(-0.652894\pi\)
0.536992 + 0.843587i \(0.319560\pi\)
\(558\) 11.9278 7.45605i 0.504943 0.315640i
\(559\) 30.7086 13.7172i 1.29884 0.580177i
\(560\) −3.82596 −0.161676
\(561\) −2.31118 2.70749i −0.0975782 0.114310i
\(562\) −7.32040 12.6793i −0.308792 0.534844i
\(563\) −17.5130 + 30.3335i −0.738087 + 1.27840i 0.215269 + 0.976555i \(0.430937\pi\)
−0.953356 + 0.301849i \(0.902396\pi\)
\(564\) 3.90290 + 13.6068i 0.164342 + 0.572949i
\(565\) −31.8280 18.3759i −1.33901 0.773080i
\(566\) 1.97645 3.42330i 0.0830762 0.143892i
\(567\) −11.4614 + 23.5191i −0.481332 + 0.987709i
\(568\) 36.4649 + 21.0530i 1.53003 + 0.883365i
\(569\) 0.907095 + 1.57113i 0.0380274 + 0.0658654i 0.884413 0.466706i \(-0.154559\pi\)
−0.846385 + 0.532571i \(0.821226\pi\)
\(570\) −8.78088 8.47819i −0.367791 0.355112i
\(571\) 7.01838i 0.293710i 0.989158 + 0.146855i \(0.0469151\pi\)
−0.989158 + 0.146855i \(0.953085\pi\)
\(572\) −11.7970 10.4187i −0.493256 0.435629i
\(573\) −7.35941 + 2.11094i −0.307444 + 0.0881858i
\(574\) −4.06135 7.03447i −0.169518 0.293613i
\(575\) −41.0003 + 23.6715i −1.70983 + 0.987170i
\(576\) 0.426624 + 12.1590i 0.0177760 + 0.506625i
\(577\) 35.3698i 1.47247i −0.676728 0.736233i \(-0.736603\pi\)
0.676728 0.736233i \(-0.263397\pi\)
\(578\) −11.8996 6.87023i −0.494958 0.285764i
\(579\) 0.416559 + 0.103823i 0.0173116 + 0.00431474i
\(580\) −31.9507 −1.32668
\(581\) 39.3486 + 22.7179i 1.63245 + 0.942498i
\(582\) −14.6835 + 15.2077i −0.608650 + 0.630381i
\(583\) −0.979648 2.15161i −0.0405729 0.0891107i
\(584\) 36.3192i 1.50290i
\(585\) −32.3977 21.7873i −1.33948 0.900793i
\(586\) 14.0386 0.579929
\(587\) 0.294905 + 0.510791i 0.0121720 + 0.0210826i 0.872047 0.489422i \(-0.162792\pi\)
−0.859875 + 0.510504i \(0.829459\pi\)
\(588\) 2.29720 2.37922i 0.0947350 0.0981172i
\(589\) 11.5934 + 6.69344i 0.477697 + 0.275798i
\(590\) 0.725386i 0.0298637i
\(591\) −1.54936 + 6.21635i −0.0637323 + 0.255707i
\(592\) −0.0821560 0.0474328i −0.00337659 0.00194948i
\(593\) 44.3988i 1.82324i −0.411034 0.911620i \(-0.634832\pi\)
0.411034 0.911620i \(-0.365168\pi\)
\(594\) −13.9137 + 3.08319i −0.570888 + 0.126505i
\(595\) 3.25106 + 5.63101i 0.133281 + 0.230849i
\(596\) 0.849871 0.490673i 0.0348121 0.0200988i
\(597\) −2.05592 7.16759i −0.0841431 0.293350i
\(598\) −7.17112 16.0539i −0.293249 0.656493i
\(599\) 22.1393i 0.904586i 0.891869 + 0.452293i \(0.149394\pi\)
−0.891869 + 0.452293i \(0.850606\pi\)
\(600\) −27.4320 26.4864i −1.11991 1.08130i
\(601\) 29.7118 17.1541i 1.21197 0.699730i 0.248781 0.968560i \(-0.419970\pi\)
0.963188 + 0.268829i \(0.0866368\pi\)
\(602\) −11.2121 + 19.4199i −0.456971 + 0.791497i
\(603\) 8.14203 + 13.0252i 0.331569 + 0.530425i
\(604\) −3.59434 + 6.22557i −0.146251 + 0.253315i
\(605\) 26.0689 29.9470i 1.05985 1.21752i
\(606\) 21.3487 6.12357i 0.867232 0.248753i
\(607\) 12.5059 + 7.22028i 0.507599 + 0.293062i 0.731846 0.681470i \(-0.238659\pi\)
−0.224247 + 0.974532i \(0.571992\pi\)
\(608\) −11.8306 + 6.83041i −0.479795 + 0.277010i
\(609\) 23.5218 24.3616i 0.953151 0.987180i
\(610\) 27.7403 1.12317
\(611\) 13.1375 18.1287i 0.531487 0.733407i
\(612\) −2.07479 + 1.29695i −0.0838684 + 0.0524261i
\(613\) 6.24909 + 10.8237i 0.252398 + 0.437167i 0.964186 0.265228i \(-0.0854474\pi\)
−0.711787 + 0.702395i \(0.752114\pi\)
\(614\) −19.1665 + 11.0658i −0.773495 + 0.446578i
\(615\) −5.10870 + 20.4971i −0.206003 + 0.826524i
\(616\) 26.3170 + 2.54323i 1.06034 + 0.102470i
\(617\) −7.25971 + 12.5742i −0.292265 + 0.506218i −0.974345 0.225060i \(-0.927742\pi\)
0.682080 + 0.731278i \(0.261076\pi\)
\(618\) 6.51592 26.1432i 0.262109 1.05163i
\(619\) 28.1176i 1.13014i −0.825042 0.565071i \(-0.808849\pi\)
0.825042 0.565071i \(-0.191151\pi\)
\(620\) 23.3276 + 13.4682i 0.936860 + 0.540896i
\(621\) 29.9743 + 6.36343i 1.20283 + 0.255356i
\(622\) −0.180752 0.313072i −0.00724751 0.0125531i
\(623\) 30.7927 1.23368
\(624\) −1.74246 + 1.46596i −0.0697541 + 0.0586856i
\(625\) −0.689408 −0.0275763
\(626\) 10.0443 5.79911i 0.401453 0.231779i
\(627\) −8.80561 10.3155i −0.351662 0.411963i
\(628\) −5.61285 + 9.72174i −0.223977 + 0.387940i
\(629\) 0.161222i 0.00642834i
\(630\) 26.0147 0.912779i 1.03645 0.0363660i
\(631\) 40.8299 + 23.5731i 1.62541 + 0.938432i 0.985438 + 0.170036i \(0.0543885\pi\)
0.639975 + 0.768396i \(0.278945\pi\)
\(632\) −0.867650 −0.0345133
\(633\) −5.45713 + 21.8951i −0.216901 + 0.870252i
\(634\) 0.947270 0.546907i 0.0376209 0.0217204i
\(635\) −40.6510 + 23.4699i −1.61319 + 0.931373i
\(636\) −1.56199 + 0.448035i −0.0619371 + 0.0177657i
\(637\) −5.20277 0.540422i −0.206141 0.0214123i
\(638\) 18.3603 + 1.77431i 0.726893 + 0.0702456i
\(639\) 40.6750 + 21.6186i 1.60908 + 0.855218i
\(640\) −25.6901 + 14.8322i −1.01549 + 0.586292i
\(641\) −15.6699 9.04702i −0.618924 0.357336i 0.157526 0.987515i \(-0.449648\pi\)
−0.776450 + 0.630179i \(0.782982\pi\)
\(642\) 13.1452 3.77050i 0.518798 0.148810i
\(643\) 39.2511 + 22.6617i 1.54791 + 0.893688i 0.998301 + 0.0582687i \(0.0185580\pi\)
0.549613 + 0.835420i \(0.314775\pi\)
\(644\) −19.5402 11.2815i −0.769992 0.444555i
\(645\) 56.0567 16.0790i 2.20723 0.633112i
\(646\) 1.04777 + 0.604927i 0.0412238 + 0.0238006i
\(647\) 9.09155 5.24901i 0.357426 0.206360i −0.310525 0.950565i \(-0.600505\pi\)
0.667951 + 0.744205i \(0.267172\pi\)
\(648\) 1.72980 + 24.6198i 0.0679531 + 0.967157i
\(649\) −0.0775317 + 0.802289i −0.00304338 + 0.0314926i
\(650\) −2.47304 + 23.8085i −0.0970006 + 0.933848i
\(651\) −27.4427 + 7.87154i −1.07556 + 0.308510i
\(652\) 15.0446 8.68599i 0.589191 0.340170i
\(653\) 39.1789 22.6199i 1.53319 0.885186i 0.533975 0.845500i \(-0.320698\pi\)
0.999212 0.0396861i \(-0.0126358\pi\)
\(654\) 2.30939 9.26574i 0.0903043 0.362319i
\(655\) −4.31055 −0.168427
\(656\) 1.06699 + 0.616025i 0.0416588 + 0.0240517i
\(657\) −1.39324 39.7081i −0.0543556 1.54916i
\(658\) 14.9271i 0.581919i
\(659\) 8.74287 15.1431i 0.340574 0.589891i −0.643966 0.765055i \(-0.722712\pi\)
0.984539 + 0.175163i \(0.0560453\pi\)
\(660\) −17.7182 20.7564i −0.689681 0.807943i
\(661\) 20.8361 12.0297i 0.810430 0.467902i −0.0366754 0.999327i \(-0.511677\pi\)
0.847105 + 0.531425i \(0.178343\pi\)
\(662\) 18.5645 0.721531
\(663\) 3.63823 + 1.31884i 0.141297 + 0.0512197i
\(664\) 42.8610 1.66333
\(665\) 12.3866 + 21.4542i 0.480331 + 0.831957i
\(666\) 0.569938 + 0.302920i 0.0220846 + 0.0117379i
\(667\) −34.3477 19.8307i −1.32995 0.767847i
\(668\) 28.0662i 1.08591i
\(669\) −1.73879 + 6.97636i −0.0672254 + 0.269722i
\(670\) 7.64140 13.2353i 0.295213 0.511324i
\(671\) 30.6812 + 2.96497i 1.18443 + 0.114461i
\(672\) 7.04569 28.2687i 0.271793 1.09049i
\(673\) −20.5488 + 11.8638i −0.792097 + 0.457317i −0.840700 0.541501i \(-0.817856\pi\)
0.0486035 + 0.998818i \(0.484523\pi\)
\(674\) 5.84008 + 10.1153i 0.224952 + 0.389627i
\(675\) −31.0077 27.9054i −1.19349 1.07408i
\(676\) 16.7449 + 3.51659i 0.644034 + 0.135254i
\(677\) 10.8608 0.417414 0.208707 0.977978i \(-0.433074\pi\)
0.208707 + 0.977978i \(0.433074\pi\)
\(678\) 10.1299 10.4916i 0.389038 0.402928i
\(679\) 37.1568 21.4525i 1.42595 0.823270i
\(680\) 5.31190 + 3.06683i 0.203702 + 0.117607i
\(681\) −14.0673 + 4.03500i −0.539061 + 0.154622i
\(682\) −12.6572 9.03490i −0.484669 0.345964i
\(683\) −16.4670 + 28.5216i −0.630091 + 1.09135i 0.357442 + 0.933935i \(0.383649\pi\)
−0.987533 + 0.157414i \(0.949684\pi\)
\(684\) −7.90496 + 4.94139i −0.302254 + 0.188939i
\(685\) −2.87186 + 4.97421i −0.109728 + 0.190055i
\(686\) −11.5528 + 6.67002i −0.441088 + 0.254662i
\(687\) −19.8872 19.2016i −0.758743 0.732588i
\(688\) 3.40130i 0.129673i
\(689\) 2.08109 + 1.50813i 0.0792831 + 0.0574550i
\(690\) −8.40584 29.3054i −0.320005 1.11564i
\(691\) −7.96732 + 4.59993i −0.303091 + 0.174990i −0.643831 0.765168i \(-0.722656\pi\)
0.340740 + 0.940158i \(0.389323\pi\)
\(692\) 6.62777 + 11.4796i 0.251950 + 0.436390i
\(693\) 28.8702 + 1.77099i 1.09669 + 0.0672742i
\(694\) 19.5004i 0.740224i
\(695\) −22.5264 13.0056i −0.854474 0.493331i
\(696\) 7.72557 30.9965i 0.292837 1.17492i
\(697\) 2.09384i 0.0793099i
\(698\) −17.4877 10.0965i −0.661917 0.382158i
\(699\) −17.4337 + 18.0562i −0.659404 + 0.682947i
\(700\) 15.3584 + 26.6015i 0.580491 + 1.00544i
\(701\) −38.1047 −1.43919 −0.719597 0.694392i \(-0.755673\pi\)
−0.719597 + 0.694392i \(0.755673\pi\)
\(702\) 11.4981 10.3836i 0.433969 0.391903i
\(703\) 0.614257i 0.0231671i
\(704\) 12.2414 5.57362i 0.461366 0.210064i
\(705\) 26.9643 27.9270i 1.01553 1.05179i
\(706\) 6.66308 + 3.84693i 0.250768 + 0.144781i
\(707\) −45.0767 −1.69529
\(708\) 0.537573 + 0.133985i 0.0202032 + 0.00503545i
\(709\) −39.8120 22.9855i −1.49517 0.863238i −0.495188 0.868786i \(-0.664901\pi\)
−0.999985 + 0.00554755i \(0.998234\pi\)
\(710\) 45.8299i 1.71997i
\(711\) −0.948609 + 0.0332839i −0.0355756 + 0.00124825i
\(712\) 25.1560 14.5238i 0.942762 0.544304i
\(713\) 16.7185 + 28.9573i 0.626112 + 1.08446i
\(714\) −2.48017 + 0.711400i −0.0928179 + 0.0266235i
\(715\) −8.56835 + 42.3038i −0.320438 + 1.58207i
\(716\) 13.7495i 0.513841i
\(717\) 0.628683 + 0.607011i 0.0234786 + 0.0226692i
\(718\) 2.07789 + 3.59902i 0.0775463 + 0.134314i
\(719\) −14.7218 8.49963i −0.549030 0.316983i 0.199701 0.979857i \(-0.436003\pi\)
−0.748731 + 0.662874i \(0.769336\pi\)
\(720\) −3.34803 + 2.09285i −0.124774 + 0.0779960i
\(721\) −27.3418 + 47.3574i −1.01826 + 1.76368i
\(722\) −9.61491 5.55117i −0.357830 0.206593i
\(723\) 8.77161 + 30.5807i 0.326220 + 1.13731i
\(724\) −11.6593 + 20.1945i −0.433314 + 0.750522i
\(725\) 26.9969 + 46.7600i 1.00264 + 1.73662i
\(726\) 9.02905 + 12.9115i 0.335099 + 0.479192i
\(727\) 10.6367 0.394494 0.197247 0.980354i \(-0.436800\pi\)
0.197247 + 0.980354i \(0.436800\pi\)
\(728\) −26.2437 + 11.7228i −0.972656 + 0.434476i
\(729\) 2.83565 + 26.8507i 0.105024 + 0.994470i
\(730\) −34.2352 + 19.7657i −1.26710 + 0.731561i
\(731\) −5.00600 + 2.89022i −0.185154 + 0.106899i
\(732\) 5.12384 20.5579i 0.189383 0.759842i
\(733\) −0.903764 −0.0333813 −0.0166906 0.999861i \(-0.505313\pi\)
−0.0166906 + 0.999861i \(0.505313\pi\)
\(734\) 15.6801 + 9.05289i 0.578762 + 0.334148i
\(735\) −8.80053 2.19344i −0.324612 0.0809063i
\(736\) −34.1212 −1.25772
\(737\) 9.86614 13.8217i 0.363424 0.509129i
\(738\) −7.40197 3.93412i −0.272470 0.144817i
\(739\) −23.8682 41.3409i −0.878006 1.52075i −0.853526 0.521051i \(-0.825540\pi\)
−0.0244805 0.999700i \(-0.507793\pi\)
\(740\) 1.23598i 0.0454354i
\(741\) 13.8617 + 5.02480i 0.509221 + 0.184591i
\(742\) −1.71356 −0.0629068
\(743\) 0.724160 0.418094i 0.0265668 0.0153384i −0.486658 0.873593i \(-0.661784\pi\)
0.513225 + 0.858254i \(0.328451\pi\)
\(744\) −18.7065 + 19.3744i −0.685815 + 0.710300i
\(745\) −2.33069 1.34562i −0.0853897 0.0492998i
\(746\) 16.8905 0.618405
\(747\) 46.8603 1.64419i 1.71453 0.0601578i
\(748\) 2.20167 + 1.57159i 0.0805011 + 0.0574629i
\(749\) −27.7554 −1.01416
\(750\) −3.78606 + 15.1904i −0.138247 + 0.554676i
\(751\) −11.3098 19.5892i −0.412701 0.714819i 0.582483 0.812843i \(-0.302081\pi\)
−0.995184 + 0.0980237i \(0.968748\pi\)
\(752\) −1.13207 1.96080i −0.0412823 0.0715031i
\(753\) 20.8094 5.96888i 0.758338 0.217518i
\(754\) −18.3092 + 8.17853i −0.666781 + 0.297844i
\(755\) 19.7142 0.717473
\(756\) 4.12867 19.4477i 0.150158 0.707305i
\(757\) −9.88087 17.1142i −0.359126 0.622025i 0.628689 0.777657i \(-0.283592\pi\)
−0.987815 + 0.155632i \(0.950259\pi\)
\(758\) 0.990299 1.71525i 0.0359693 0.0623006i
\(759\) −6.16472 33.3107i −0.223765 1.20910i
\(760\) 20.2384 + 11.6846i 0.734123 + 0.423846i
\(761\) 31.4569 + 18.1616i 1.14031 + 0.658358i 0.946507 0.322682i \(-0.104584\pi\)
0.193803 + 0.981041i \(0.437918\pi\)
\(762\) −5.13569 17.9047i −0.186046 0.648617i
\(763\) −9.69056 + 16.7845i −0.350822 + 0.607641i
\(764\) 5.03840 2.90892i 0.182283 0.105241i
\(765\) 5.92519 + 3.14922i 0.214226 + 0.113860i
\(766\) 7.86930i 0.284330i
\(767\) −0.357375 0.800053i −0.0129041 0.0288882i
\(768\) −7.11904 24.8192i −0.256886 0.895588i
\(769\) −7.14901 12.3825i −0.257800 0.446523i 0.707852 0.706360i \(-0.249664\pi\)
−0.965652 + 0.259838i \(0.916331\pi\)
\(770\) −11.9250 26.1910i −0.429747 0.943858i
\(771\) 4.14599 16.6346i 0.149314 0.599079i
\(772\) −0.326222 −0.0117410
\(773\) −12.6620 + 21.9313i −0.455421 + 0.788813i −0.998712 0.0507315i \(-0.983845\pi\)
0.543291 + 0.839545i \(0.317178\pi\)
\(774\) 0.811467 + 23.1272i 0.0291676 + 0.831291i
\(775\) 45.5201i 1.63513i
\(776\) 20.2368 35.0511i 0.726458 1.25826i
\(777\) −0.942400 0.909914i −0.0338084 0.0326430i
\(778\) −4.22567 7.31907i −0.151498 0.262401i
\(779\) 7.97755i 0.285825i
\(780\) 27.8918 + 10.1107i 0.998685 + 0.362020i
\(781\) 4.89845 50.6886i 0.175280 1.81378i
\(782\) 1.51095 + 2.61705i 0.0540316 + 0.0935855i
\(783\) 7.25737 34.1851i 0.259357 1.22168i
\(784\) −0.264493 + 0.458115i −0.00944618 + 0.0163613i
\(785\) 30.7853 1.09878
\(786\) 0.413673 1.65974i 0.0147552 0.0592010i
\(787\) −24.5633 + 42.5448i −0.875586 + 1.51656i −0.0194488 + 0.999811i \(0.506191\pi\)
−0.856137 + 0.516749i \(0.827142\pi\)
\(788\) 4.86825i 0.173424i
\(789\) −18.7414 4.67110i −0.667211 0.166295i
\(790\) 0.472193 + 0.817863i 0.0167999 + 0.0290983i
\(791\) −25.6339 + 14.7998i −0.911438 + 0.526219i
\(792\) 24.4208 12.1703i 0.867754 0.432451i
\(793\) −30.5956 + 13.6668i −1.08648 + 0.485321i
\(794\) −24.3275 −0.863350
\(795\) 3.20588 + 3.09537i 0.113701 + 0.109782i
\(796\) 2.83310 + 4.90708i 0.100417 + 0.173927i
\(797\) −0.534561 0.308629i −0.0189351 0.0109322i 0.490503 0.871440i \(-0.336813\pi\)
−0.509438 + 0.860508i \(0.670147\pi\)
\(798\) −9.44945 + 2.71044i −0.334507 + 0.0959484i
\(799\) −1.92393 + 3.33234i −0.0680637 + 0.117890i
\(800\) 40.2283 + 23.2258i 1.42228 + 0.821156i
\(801\) 26.9461 16.8440i 0.952095 0.595155i
\(802\) 13.9564 + 8.05771i 0.492816 + 0.284528i
\(803\) −39.9772 + 18.2020i −1.41077 + 0.642334i
\(804\) −8.39705 8.10759i −0.296141 0.285933i
\(805\) 61.8770i 2.18088i
\(806\) 16.8153 + 1.74664i 0.592293 + 0.0615226i
\(807\) −0.379209 + 0.108770i −0.0133488 + 0.00382890i
\(808\) −36.8253 + 21.2611i −1.29551 + 0.747964i
\(809\) 8.26616 + 14.3174i 0.290623 + 0.503373i 0.973957 0.226732i \(-0.0728042\pi\)
−0.683334 + 0.730105i \(0.739471\pi\)
\(810\) 22.2657 15.0292i 0.782336 0.528071i
\(811\) 26.7650 0.939846 0.469923 0.882707i \(-0.344282\pi\)
0.469923 + 0.882707i \(0.344282\pi\)
\(812\) −12.8664 + 22.2852i −0.451522 + 0.782058i
\(813\) −8.60947 2.14582i −0.301947 0.0752573i
\(814\) 0.0686372 0.710249i 0.00240573 0.0248942i
\(815\) −41.2582 23.8205i −1.44521 0.834394i
\(816\) 0.271839 0.281544i 0.00951626 0.00985602i
\(817\) −19.0729 + 11.0117i −0.667276 + 0.385252i
\(818\) 22.5089i 0.787004i
\(819\) −28.2427 + 13.8234i −0.986881 + 0.483027i
\(820\) 16.0520i 0.560562i
\(821\) 13.7604 7.94457i 0.480241 0.277268i −0.240276 0.970705i \(-0.577238\pi\)
0.720517 + 0.693437i \(0.243905\pi\)
\(822\) −1.63967 1.58315i −0.0571901 0.0552186i
\(823\) 11.3951 19.7368i 0.397207 0.687982i −0.596173 0.802856i \(-0.703313\pi\)
0.993380 + 0.114873i \(0.0366463\pi\)
\(824\) 51.5847i 1.79704i
\(825\) −15.4060 + 43.4690i −0.536369 + 1.51340i
\(826\) 0.505948 + 0.292109i 0.0176042 + 0.0101638i
\(827\) 20.8987i 0.726718i 0.931649 + 0.363359i \(0.118370\pi\)
−0.931649 + 0.363359i \(0.881630\pi\)
\(828\) −23.2704 + 0.816492i −0.808704 + 0.0283751i
\(829\) 1.27661 + 2.21115i 0.0443384 + 0.0767963i 0.887343 0.461110i \(-0.152549\pi\)
−0.843005 + 0.537906i \(0.819215\pi\)
\(830\) −23.3259 40.4016i −0.809652 1.40236i
\(831\) 1.56856 0.449919i 0.0544129 0.0156075i
\(832\) −8.58035 + 11.8402i −0.297470 + 0.410484i
\(833\) 0.899000 0.0311485
\(834\) 7.16950 7.42546i 0.248259 0.257123i
\(835\) 66.6568 38.4843i 2.30675 1.33180i
\(836\) 8.38838 + 5.98775i 0.290118 + 0.207091i
\(837\) −19.7088 + 21.8998i −0.681235 + 0.756968i
\(838\) −9.36016 + 16.2123i −0.323341 + 0.560044i
\(839\) 26.0038 45.0399i 0.897751 1.55495i 0.0673887 0.997727i \(-0.478533\pi\)
0.830362 0.557224i \(-0.188133\pi\)
\(840\) −47.9063 + 13.7412i −1.65292 + 0.474117i
\(841\) −8.11652 + 14.0582i −0.279880 + 0.484766i
\(842\) −6.76474 11.7169i −0.233128 0.403790i
\(843\) 22.0607 + 21.3002i 0.759811 + 0.733619i
\(844\) 17.1468i 0.590218i
\(845\) −14.6087 44.5909i −0.502555 1.53397i
\(846\) 8.16533 + 13.0624i 0.280730 + 0.449096i
\(847\) −10.3898 30.2422i −0.356999 1.03914i
\(848\) 0.225091 0.129956i 0.00772965 0.00446272i
\(849\) −2.00231 + 8.03366i −0.0687190 + 0.275714i
\(850\) 4.11394i 0.141107i
\(851\) −0.767128 + 1.32870i −0.0262968 + 0.0455474i
\(852\) −33.9639 8.46515i −1.16358 0.290011i
\(853\) 36.8393 1.26135 0.630677 0.776045i \(-0.282777\pi\)
0.630677 + 0.776045i \(0.282777\pi\)
\(854\) 11.1709 19.3485i 0.382259 0.662092i
\(855\) 22.5750 + 11.9985i 0.772049 + 0.410341i
\(856\) −22.6747 + 13.0912i −0.775005 + 0.447449i
\(857\) −38.8835 −1.32823 −0.664117 0.747629i \(-0.731192\pi\)
−0.664117 + 0.747629i \(0.731192\pi\)
\(858\) −15.4664 7.35896i −0.528015 0.251231i
\(859\) −32.7312 −1.11677 −0.558387 0.829581i \(-0.688580\pi\)
−0.558387 + 0.829581i \(0.688580\pi\)
\(860\) −38.3776 + 22.1573i −1.30866 + 0.755557i
\(861\) 12.2393 + 11.8173i 0.417113 + 0.402734i
\(862\) 1.39156 2.41026i 0.0473969 0.0820938i
\(863\) 25.4617 0.866726 0.433363 0.901219i \(-0.357327\pi\)
0.433363 + 0.901219i \(0.357327\pi\)
\(864\) −9.29783 28.5915i −0.316319 0.972704i
\(865\) 18.1760 31.4817i 0.618002 1.07041i
\(866\) 29.6172i 1.00643i
\(867\) 27.9255 + 6.96013i 0.948398 + 0.236379i
\(868\) 18.7878 10.8472i 0.637701 0.368177i
\(869\) 0.434837 + 0.955039i 0.0147508 + 0.0323975i
\(870\) −33.4223 + 9.58670i −1.13312 + 0.325020i
\(871\) −1.90733 + 18.3623i −0.0646275 + 0.622184i
\(872\) 18.2828i 0.619134i
\(873\) 20.7804 39.0980i 0.703311 1.32327i
\(874\) 5.75674 + 9.97097i 0.194725 + 0.337273i
\(875\) 15.8869 27.5169i 0.537075 0.930240i
\(876\) 8.32455 + 29.0220i 0.281260 + 0.980564i
\(877\) 3.21508 5.56869i 0.108566 0.188041i −0.806624 0.591065i \(-0.798708\pi\)
0.915189 + 0.403024i \(0.132041\pi\)
\(878\) −13.2552 + 22.9586i −0.447340 + 0.774816i
\(879\) −28.2644 + 8.10724i −0.953336 + 0.273450i
\(880\) 3.55277 + 2.53602i 0.119764 + 0.0854893i
\(881\) 4.66499 2.69334i 0.157168 0.0907408i −0.419353 0.907823i \(-0.637743\pi\)
0.576521 + 0.817082i \(0.304410\pi\)
\(882\) 1.68913 3.17807i 0.0568760 0.107011i
\(883\) −1.74325 −0.0586651 −0.0293326 0.999570i \(-0.509338\pi\)
−0.0293326 + 0.999570i \(0.509338\pi\)
\(884\) −2.92495 0.303821i −0.0983767 0.0102186i
\(885\) −0.418908 1.46045i −0.0140814 0.0490924i
\(886\) 6.93929 + 12.0192i 0.233130 + 0.403793i
\(887\) −24.6417 42.6807i −0.827388 1.43308i −0.900080 0.435724i \(-0.856492\pi\)
0.0726924 0.997354i \(-0.476841\pi\)
\(888\) −1.19907 0.298855i −0.0402380 0.0100289i
\(889\) 37.8048i 1.26793i
\(890\) −27.3809 15.8084i −0.917809 0.529897i
\(891\) 26.2326 14.2427i 0.878824 0.477147i
\(892\) 5.46344i 0.182930i
\(893\) −7.33018 + 12.6962i −0.245295 + 0.424863i
\(894\) 0.741790 0.768274i 0.0248092 0.0256949i
\(895\) 32.6548 18.8532i 1.09153 0.630195i
\(896\) 23.8913i 0.798153i
\(897\) 23.7090 + 28.1806i 0.791619 + 0.940924i
\(898\) 4.58874i 0.153128i
\(899\) 33.0252 19.0671i 1.10145 0.635924i
\(900\) 27.9912 + 14.8772i 0.933040 + 0.495908i
\(901\) −0.382537 0.220858i −0.0127442 0.00735784i
\(902\) −0.891414 + 9.22424i −0.0296808 + 0.307134i
\(903\) 11.3588 45.5738i 0.377998 1.51660i
\(904\) −13.9611 + 24.1813i −0.464338 + 0.804257i
\(905\) 63.9488 2.12573
\(906\) −1.89192 + 7.59078i −0.0628550 + 0.252187i
\(907\) 3.86028 + 6.68620i 0.128179 + 0.222012i 0.922971 0.384870i \(-0.125754\pi\)
−0.794792 + 0.606881i \(0.792420\pi\)
\(908\) 9.63077 5.56033i 0.319608 0.184526i
\(909\) −39.4459 + 24.6576i −1.30834 + 0.817842i
\(910\) 25.3325 + 18.3580i 0.839764 + 0.608562i
\(911\) 12.0195i 0.398225i −0.979977 0.199113i \(-0.936194\pi\)
0.979977 0.199113i \(-0.0638060\pi\)
\(912\) 1.03571 1.07268i 0.0342957 0.0355201i
\(913\) −21.4805 47.1779i −0.710901 1.56136i
\(914\) −13.9222 8.03796i −0.460504 0.265872i
\(915\) −55.8505 + 16.0199i −1.84636 + 0.529602i
\(916\) 18.1922 + 10.5033i 0.601087 + 0.347038i
\(917\) −1.73584 + 3.00656i −0.0573224 + 0.0992853i
\(918\) −1.78121 + 1.97922i −0.0587885 + 0.0653240i
\(919\) 1.02543 + 0.592032i 0.0338258 + 0.0195293i 0.516818 0.856096i \(-0.327117\pi\)
−0.482992 + 0.875625i \(0.660450\pi\)
\(920\) 29.1852 + 50.5503i 0.962208 + 1.66659i
\(921\) 32.1981 33.3477i 1.06096 1.09884i
\(922\) 3.49756 0.115186
\(923\) 22.5790 + 50.5474i 0.743197 + 1.66379i
\(924\) −21.6124 + 3.99975i −0.710996 + 0.131582i
\(925\) 1.80886 1.04435i 0.0594749 0.0343379i
\(926\) 0.532897 + 0.923005i 0.0175121 + 0.0303318i
\(927\) 1.97884 + 56.3980i 0.0649937 + 1.85235i
\(928\) 38.9146i 1.27743i
\(929\) 11.4306 19.7984i 0.375027 0.649565i −0.615304 0.788290i \(-0.710967\pi\)
0.990331 + 0.138724i \(0.0443002\pi\)
\(930\) 28.4432 + 7.08917i 0.932688 + 0.232463i
\(931\) 3.42520 0.112256
\(932\) 9.53623 16.5172i 0.312370 0.541040i
\(933\) 0.544714 + 0.525937i 0.0178331 + 0.0172184i
\(934\) −3.07485 5.32580i −0.100612 0.174265i
\(935\) 0.713566 7.38390i 0.0233361 0.241479i
\(936\) −16.5529 + 24.6141i −0.541047 + 0.804537i
\(937\) 32.3201i 1.05585i 0.849291 + 0.527925i \(0.177030\pi\)
−0.849291 + 0.527925i \(0.822970\pi\)
\(938\) −6.15431 10.6596i −0.200945 0.348047i
\(939\) −16.8737 + 17.4761i −0.550653 + 0.570312i
\(940\) −14.7494 + 25.5467i −0.481073 + 0.833243i
\(941\) 8.07497i 0.263237i 0.991300 + 0.131618i \(0.0420173\pi\)
−0.991300 + 0.131618i \(0.957983\pi\)
\(942\) −2.95439 + 11.8536i −0.0962594 + 0.386212i
\(943\) 9.96294 17.2563i 0.324438 0.561943i
\(944\) −0.0886142 −0.00288415
\(945\) −51.8492 + 16.8611i −1.68666 + 0.548492i
\(946\) 23.2840 10.6014i 0.757027 0.344681i
\(947\) 13.4187 + 23.2418i 0.436048 + 0.755257i 0.997381 0.0723334i \(-0.0230446\pi\)
−0.561333 + 0.827590i \(0.689711\pi\)
\(948\) 0.693324 0.198870i 0.0225181 0.00645899i
\(949\) 28.0211 38.6668i 0.909605 1.25518i
\(950\) 15.6741i 0.508536i
\(951\) −1.59134 + 1.64815i −0.0516027 + 0.0534450i
\(952\) 4.27815 2.46999i 0.138656 0.0800529i
\(953\) 19.3102 33.4463i 0.625519 1.08343i −0.362921 0.931820i \(-0.618221\pi\)
0.988440 0.151611i \(-0.0484460\pi\)
\(954\) −1.49951 + 0.937342i −0.0485483 + 0.0303476i
\(955\) −13.8173 7.97743i −0.447118 0.258144i
\(956\) −0.575100 0.332034i −0.0186001 0.0107388i
\(957\) −37.9902 + 7.03075i −1.22805 + 0.227272i
\(958\) 3.48182 6.03069i 0.112492 0.194843i
\(959\) 2.31297 + 4.00618i 0.0746896 + 0.129366i
\(960\) −17.6109 + 18.2396i −0.568388 + 0.588681i
\(961\) −1.14954 −0.0370820
\(962\) 0.316377 + 0.708270i 0.0102004 + 0.0228355i
\(963\) −24.2882 + 15.1826i −0.782677 + 0.489252i
\(964\) −12.0875 20.9361i −0.389312 0.674307i
\(965\) 0.447316 + 0.774774i 0.0143996 + 0.0249409i
\(966\) −23.8252 5.93818i −0.766563 0.191058i
\(967\) −55.0591 −1.77058 −0.885291 0.465038i \(-0.846041\pi\)
−0.885291 + 0.465038i \(0.846041\pi\)
\(968\) −22.7522 19.8058i −0.731282 0.636583i
\(969\) −2.45885 0.612843i −0.0789896 0.0196874i
\(970\) −44.0531 −1.41446
\(971\) −24.8428 14.3430i −0.797242 0.460288i 0.0452637 0.998975i \(-0.485587\pi\)
−0.842506 + 0.538687i \(0.818921\pi\)
\(972\) −7.02524 19.2768i −0.225335 0.618303i
\(973\) −18.1425 + 10.4746i −0.581622 + 0.335800i
\(974\) −4.43617 −0.142144
\(975\) −8.77028 49.3628i −0.280874 1.58088i
\(976\) 3.38879i 0.108473i
\(977\) −27.3007 47.2861i −0.873425 1.51282i −0.858431 0.512929i \(-0.828560\pi\)
−0.0149944 0.999888i \(-0.504773\pi\)
\(978\) 13.1313 13.6001i 0.419893 0.434884i
\(979\) −28.5940 20.4108i −0.913869 0.652333i
\(980\) 6.89201 0.220157
\(981\) 0.701346 + 19.9887i 0.0223923 + 0.638191i
\(982\) 24.5854 + 14.1944i 0.784552 + 0.452961i
\(983\) −13.2851 −0.423730 −0.211865 0.977299i \(-0.567954\pi\)
−0.211865 + 0.977299i \(0.567954\pi\)
\(984\) 15.5727 + 3.88133i 0.496438 + 0.123732i
\(985\) −11.5620 + 6.67534i −0.368397 + 0.212694i
\(986\) 2.98469 1.72321i 0.0950520 0.0548783i
\(987\) −8.62035 30.0533i −0.274389 0.956607i
\(988\) −11.1441 1.15756i −0.354540 0.0368268i
\(989\) −55.0090 −1.74919
\(990\) −24.7622 16.3961i −0.786994 0.521104i
\(991\) −12.9944 22.5070i −0.412782 0.714959i 0.582411 0.812894i \(-0.302109\pi\)
−0.995193 + 0.0979356i \(0.968776\pi\)
\(992\) 16.4037 28.4121i 0.520818 0.902084i
\(993\) −37.3767 + 10.7209i −1.18611 + 0.340219i
\(994\) −31.9658 18.4555i −1.01389 0.585372i
\(995\) 7.76950 13.4572i 0.246310 0.426621i
\(996\) −34.2495 + 9.82395i −1.08524 + 0.311284i
\(997\) 28.2165 + 16.2908i 0.893625 + 0.515935i 0.875126 0.483894i \(-0.160778\pi\)
0.0184985 + 0.999829i \(0.494111\pi\)
\(998\) 3.87799 + 6.71688i 0.122756 + 0.212619i
\(999\) −1.32241 0.280743i −0.0418393 0.00888232i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 429.2.t.a.296.20 yes 104
3.2 odd 2 inner 429.2.t.a.296.33 yes 104
11.10 odd 2 inner 429.2.t.a.296.34 yes 104
13.4 even 6 inner 429.2.t.a.329.19 yes 104
33.32 even 2 inner 429.2.t.a.296.19 104
39.17 odd 6 inner 429.2.t.a.329.34 yes 104
143.43 odd 6 inner 429.2.t.a.329.33 yes 104
429.329 even 6 inner 429.2.t.a.329.20 yes 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.t.a.296.19 104 33.32 even 2 inner
429.2.t.a.296.20 yes 104 1.1 even 1 trivial
429.2.t.a.296.33 yes 104 3.2 odd 2 inner
429.2.t.a.296.34 yes 104 11.10 odd 2 inner
429.2.t.a.329.19 yes 104 13.4 even 6 inner
429.2.t.a.329.20 yes 104 429.329 even 6 inner
429.2.t.a.329.33 yes 104 143.43 odd 6 inner
429.2.t.a.329.34 yes 104 39.17 odd 6 inner